If the `gcd` of `x^2 + 10x + (p + 6) and x^2 + (p/3) x + 8 ` is `x+4` find p

If P = ( x ^(2) - 36)/( x ^(2) - 49) and Q = ( x + 6)/(x - 7) , then find the vlaue of ( P )/( Q).

If P (x) = (x ^(3) - 8) (x +1) and Q (x) = (x ^(3) +1) (x - 2), then find the LCM of P (x) and Q (x).

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: (i) p(x) = x^3 - 3x^2 + 5x - 3, g(x) = x^2 - 2 (ii) p(x) = x^4 - 3x^2 + 4x - 5, g(x) = x^2 + 1 - x (iii) p(x) = x^4 - 5x + 6, g(x) = 2 - x^2

If X ~ B (6,p) and 2. P (X =3) =P (X= 2) then find the value of p

If P = 8x^(4) + 6x^(3) - 15 x^(2) + 27 x - 20 and Q = 2x^(2) + 3x - 4 , then find the remainder when P is divided by Q .

simplify: (i) 2p^(3) - 3p^(2) + 4p - 5- 6p^(3) + 2p^(2) - 8p - 2 + 6p + 8 (ii) 2x^(2) - xy + 6x - 4y + 5xy - 4x + 6x^(2) + 3y (iii) x^(4) - 6x^(3) + 2x - 7 + 7x^(3) - x + 5x^(2) + 2 - x^(4)

If (x + 6) is a factor of f (x) = x ^(3) + 3x ^(2) + 4x + P, then find the value of P.